Non-uniform motion — practice questions

Identify knowns and unknowns: Mass ($m$) = 2.5 kg Initial velocity ($u$) = 0 m/s (from rest) Final velocity ($v$) = 15 m/s Time ($t$) = 3.0 s Resultant force ($F_{resultant}$) = ?

Calculate the acceleration ($a$): Using the kinematic equation: $a = \frac{v - u}{t}$ $a = \frac{15 \text{ m/s} - 0 \text{ m/s}}{3.0 \text{ s}}$ $a = 5.0 \text{ m/s}^2$

Apply Newton's Second Law ($F_{resultant} = ma$): $F_{resultant} = 2.5 \text{ kg} \times 5.0 \text{ m/s}^2$ $F_{resultant} = 12.5 \text{ N}$

The magnitude of the resultant force is 12.5 N.

(a) Calculate the weight: Weight is the force due to gravity. Formula: $W = mg$ $W = (80.0 \text{ kg}) \times (9.81 \text{ m/s}^2)$ $W = 784.8 \text{ N}$ The skydiver's weight is 785 N (to 3 s.f.).

(b) Calculate resultant force and acceleration: The forces acting are weight (downwards) and air resistance (upwards). We'll take downwards as the positive direction. Resultant Force ($F_{net}$) = Weight - Air Resistance $F_{net} = 784.8 \text{ N} - 600 \text{ N}$ $F_{net} = 184.8 \text{ N}$ The resultant downward force is 185 N (to 3 s.f.).

Now, use Newton's Second Law to find acceleration ($a$). Formula: $F_{net} = ma$ $a = \frac{F_{net}}{m}$ $a = \frac{184.8 \text{ N}}{80.0 \text{ kg}}$ $a = 2.31 \text{ m/s}^2$ The skydiver's acceleration at this instant is 2.31 m/s² downwards.

(c) Air resistance at terminal velocity: By definition, terminal velocity is reached when the resultant force is zero. This means the upward forces balance the downward forces. Air Resistance = Weight Air Resistance = 784.8 N The magnitude of the air resistance at terminal velocity is 785 N (to 3 s.f.).